Inkspill Magazine is holding its first ever Short Story Competition to, in their words, 'give you the chance to get your hands on some cash'. Not a great deal of cash, it has to be said; the total prize money is just £100 with £70 going to the first prize winner.
On the other hand, the bonus is that even if you don't win a cash prize you will get something back. The magazine's editors have promised that every entry will receive a short critique. They don't say how short, but for an entry fee of just £3 (£5 after 1 October) it seems to me a cheap price to pay for some independent feedback on your work AND the chance to win some cash and get your story published.
So if the Sunday Times Competition isn't for you, maybe this one is. See here for rules and information.